Physics

Problem

A space agency compares three locations relative to the Earth’s surface: • Station P: altitude

400\,\text{km}

(

h = 4.00 \times 10^5\,\text{m}

), • Station Q: an underground laboratory at an unknown depth

d

, • Station R: a weather balloon rising to an altitude

h_R

. Take

R_E = 6.4 \times 10^6\,\text{m}

and

g = 9.8\,\text{m}\,\text{s}^{-2}

at the surface. a. (i) Calculate

g_P

, the gravitational acceleration at Station P. b. (ii) If

g_Q

equals

g_P

, compute the required depth

d

for Station Q. c. (iii) Station R is to be located so that

g_R

is exactly midway between the surface value and

g_P

. Determine the altitude

h_R

that satisfies this condition. d. (iv) Between Stations Q and R, indicate which one is closer (in linear distance) to the Earth’s surface and support your answer with numerical values.

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